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The shrinking populations of many regions in Portugal have led to a debate on the criteria which should guide the restructuring of public services at the local scale, and namely how to balance raising per capita costs with guaranteeing equity in accessibility. This article contributes to this debate by analyzing the spatial distribution of primary schools in the municipality of Vagos. It is based on a linear programming approach to optimize the resources needed for the operation and installation of school facilities and the level of accessibility that is provided. The simulated configurations are used as benchmarks for the actual spatial distribution of schools, identifying how it could be made more efficient or equitable and the criteria which have been prioritized in recent school planning policies. This allowed to conclude that, in the analyzed context, changes to the spatial distribution of schools have been made with significant equity concerns and that, while it would be possible to decrease costs through further consolidation, this would pose significant equity challenges.

Equity, fairness, and justice are related concepts widely discussed in several areas of study but remain an open field in terms of spatial justice and support decision systems application. Uneven spatial development have shown a tendency to amplify social inequalities alongside territories. To better understand the spatial configuration and spatial distribution of resources for different social groups, multiple objective criteria can be used to formulate optimal resource allocation. This work discusses spatial justice by utilitarianism and Rawlsian difference principle perspectives to formulate two models based on facility location problem (FLP) framework. Assuming the proximity to a desired opportunity (service or resource) as a measure of wellbeing and satisfaction, we weight the distances to the nearest facility by a social factor based on exponential function. Optimization results tend to favor outliers for weighted FLP, while the regular distances FLP formulation tend to favor heavy urban areas. We found that results are heavy context based, as the distribution of social groups are determinant in optimization process.

Social inequalities have shown a tendency for being amplified by the distribution of socio‐economic groups and of spatial amenities and disamenities. Given their commitment to principles of spatial equity, it is important to understand if public services fit into this pattern or, on the contrary, provide similar levels of accessibility to different socio‐economic groups. This paper analyses the relationship between the location of primary schools and the spatial distribution of socio‐economic groups in Portugal and it concludes that there is a systematic tendency for disadvantaged populations to have worse accessibility than advantaged ones, independently of spatial scales and types of territories.

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